On symmetric, smooth and Calabi–Yau algebras
On symmetric, smooth and Calabi–Yau algebras
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关于对称、光滑和 Calabi-Yau 代数
DOI：
10.1016/j.jalgebra.2007.08.021
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发表时间：
2007
影响因子：
0.9
通讯作者：
A. Braun
中科院分区：
文献类型：
--
作者：
A. Braun
卡-丘代数的一个可能的定义是对称光滑PI代数。本文的主要目的是证明光滑PI代数中（局部）对称性的充分必要条件。许多已知的光滑PI代数都具有这一性质。特别是复半单李代数的量子包络代数，在单位根的情况下和sl（n）的包络代数，其中（p，n）=1，在特征p中，是典型的例子。一个令人惊讶的结果是，inj.dimT，是有限的，其中T是零特征域上m，n×n一般矩阵的迹环.
One possible definition for a Calabi–Yau algebra is a symmetric smooth PI algebra. Our main purpose here is to prove some necessary and sufficient criteria for verifying the (local) symmetric property, in smooth PI algebras. Many known smooth PI algebras are shown to have this property. In particular quantum enveloping algebras of complex semi-simple Lie algebras, in the root of unity case and the enveloping algebra of sl(n) with (p,n)=1, in characteristic p, are typical examples. A surprising result is that the inj.dimT, is finite, where T is the trace ring of m, n×n generic matrices over a field of zero characteristic.